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Regularity in Campanato spaces for solutions of fully nonlinear elliptic systems
Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials
1. | University of Texas at Austin, Department of Mathematics, 2515 Speedway Stop C1200, Austin, TX 78712-1202, United States |
2. | Université Paris-Dauphine, CEREMADE UMR CNRS 7534, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France |
References:
[1] |
L. Ambrosio and A. Figalli, Geodesics in the space of measure-preserving maps and plans, Arch. Ration. Mech. Anal., 194 (2009), 421-462.
doi: 10.1007/s00205-008-0189-2. |
[2] |
L. Ambrosio and A. Figalli, On the regularity of the pressure field of Brenier's weak solutions to incompressible Euler equations, Calc. Var. Partial Differential Equations, 31 (2008), 497-509. |
[3] |
L. Ambrosio, N. Fusco and D. Pallara, "Functions of Bounded Variation and Free Discontinuity Problems," Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 2000. |
[4] |
V. Arnold, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits (French), Ann. Inst. Fourier (Grenoble), 16 (1966), 319-361.
doi: 10.5802/aif.233. |
[5] |
Y. Brenier, The least action principle and the related concept of generalized flows for incompressible perfect fluids, J. Amer. Mat. Soc., 2 (1989), 225-255.
doi: 10.1090/S0894-0347-1989-0969419-8. |
[6] |
P. Cannarsa and C. Sinestrari, "Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control," Progress in Nonlinear Differential Equations and their Applications, 58, Birkhäuser Boston, Inc., Boston, MA, 2004. |
[7] |
C. Dellacherie and P.-A. Meyer, "Probabilities and Potential," North-Holland Mathematics Studies, 29, North-Holland Publishing Co., Amsterdam-New York, 1978. |
[8] |
D. G. Ebin and J. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Annals of Math. (2), 92 (1970), 102-163.
doi: 10.2307/1970699. |
[9] |
P. Mattila, "Geometry of Sets and Measures in Euclidean Spaces. Fractals and Rectifiability," Cambridge Studies in Advanced Mathematics, 44, Cambridge University Press, Cambridge, 1995. |
[10] |
A. I. Shnirel'man, The geometry of the group of diffeomorphisms and the dynamics of an ideal incompressible fluid (Russian), Mat. Sb. (N.S.), 128 (1985), 82-109. |
[11] |
A. I. Shnirel'man, Generalized fluid flows, their approximation and applications, Geom. Funct. Anal., 4 (1994), 586-620.
doi: 10.1007/BF01896409. |
show all references
References:
[1] |
L. Ambrosio and A. Figalli, Geodesics in the space of measure-preserving maps and plans, Arch. Ration. Mech. Anal., 194 (2009), 421-462.
doi: 10.1007/s00205-008-0189-2. |
[2] |
L. Ambrosio and A. Figalli, On the regularity of the pressure field of Brenier's weak solutions to incompressible Euler equations, Calc. Var. Partial Differential Equations, 31 (2008), 497-509. |
[3] |
L. Ambrosio, N. Fusco and D. Pallara, "Functions of Bounded Variation and Free Discontinuity Problems," Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 2000. |
[4] |
V. Arnold, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits (French), Ann. Inst. Fourier (Grenoble), 16 (1966), 319-361.
doi: 10.5802/aif.233. |
[5] |
Y. Brenier, The least action principle and the related concept of generalized flows for incompressible perfect fluids, J. Amer. Mat. Soc., 2 (1989), 225-255.
doi: 10.1090/S0894-0347-1989-0969419-8. |
[6] |
P. Cannarsa and C. Sinestrari, "Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control," Progress in Nonlinear Differential Equations and their Applications, 58, Birkhäuser Boston, Inc., Boston, MA, 2004. |
[7] |
C. Dellacherie and P.-A. Meyer, "Probabilities and Potential," North-Holland Mathematics Studies, 29, North-Holland Publishing Co., Amsterdam-New York, 1978. |
[8] |
D. G. Ebin and J. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Annals of Math. (2), 92 (1970), 102-163.
doi: 10.2307/1970699. |
[9] |
P. Mattila, "Geometry of Sets and Measures in Euclidean Spaces. Fractals and Rectifiability," Cambridge Studies in Advanced Mathematics, 44, Cambridge University Press, Cambridge, 1995. |
[10] |
A. I. Shnirel'man, The geometry of the group of diffeomorphisms and the dynamics of an ideal incompressible fluid (Russian), Mat. Sb. (N.S.), 128 (1985), 82-109. |
[11] |
A. I. Shnirel'man, Generalized fluid flows, their approximation and applications, Geom. Funct. Anal., 4 (1994), 586-620.
doi: 10.1007/BF01896409. |
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